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Optimal seedings in elimination tournaments

Author

Listed:
  • Groh, Christian
  • Moldovanu, Benny
  • Sela, Aner
  • Sunde, Uwe

Abstract

We study an elimination tournament with heterogenous contestants whose ability is common-knowledge. Each pair-wise match is modeled as an all-pay auction. Equilibrium efforts are in mixed strategies, yielding complex dynamics: endogenous win probabilities in each match depend on other matches’ outcome through the identity of the expected opponent in the next round. The designer seeds competitors according to their ranks. For tournaments with four players we find optimal seedings for three different criteria: (1) maximization of total tournament effort; (2) maximization of the probability of a final among the two top ranked teams; (3) maximization of the win probability for the top player. We also find the seedings ensuring that higher ranked players have a higher winning probability. We compare our predictions with data from NCAA basketball tournaments.

Suggested Citation

  • Groh, Christian & Moldovanu, Benny & Sela, Aner & Sunde, Uwe, 2012. "Optimal seedings in elimination tournaments," Munich Reprints in Economics 20441, University of Munich, Department of Economics.
    • Handle: RePEc:lmu:muenar:20441
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    JEL classification:

    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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